Recall that malformed OWL restrictions are things like
_:x owl:onProperty ex:pa .
_:x owl:onProperty ex:pb .
_:x owl:minCardinality xsd:integer"5" .
_:x owl:allValuesFrom ex:ca .
I do not believe that there is any way to make these things work nicely.
They should never happen, but they do need to be handled in the
RDFS-compatible OWL model theory.
Right now there are two different ways of treating such junk.
1/ In the DAML+OIL model theory and in my earlier RDFS-compatible model
theories for OWL, the effect of such collections of triples is to force
all legal restrictions that can be formed from the triples to be
co-extensional.
For example, the above four triples would imply that the following four sets
{u in IOT | card({v : <u,v> in IEXT(IS(ex:pa))}) >= 5 }
{u in IOT | card({v : <u,v> in IEXT(IS(ex:pb))}) >= 5 }
{u in IOT | <u,v> in IEXT(IS(ex:pa)) -> v in ICEXT(IS(ex:ca)) }
{u in IOT | <u,v> in IEXT(IS(ex:pb)) -> v in ICEXT(IS(ex:ca)) }
are all the same.
2/ In Pat's model theories for OWL, and in the current semantics document,
the effect of such collections is to force the properties to be the
same, and then to force co-extensionality.
For example, the above four triples would imply IS(ex:pa) = IS(ex:pb)
*and* that the following two sets
{u in IOT | card({v : <u,v> in IEXT(IS(ex:pa))}) >= 5 }
{u in IOT | <u,v> in IEXT(IS(ex:pa)) -> v in ICEXT(IS(ex:ca)) }
are the same.
I PROPOSE to use the DAML+OIL solution because I find that forcing the
properties to be the same commits more violence than just forcing the
various extensions to be the same.
Note that the entire issue does not arise in the abstract syntax as there
is no way of creating such malformed restrictions there.
Peter F. Patel-Schneider
Bell Labs Research